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Properties

Label 40T240451
Degree $40$
Order $1310720000$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^{16}.C_5^2.D_5:F_5.C_2^2$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 240451);
 

Group invariants

Abstract group:  $C_2^{16}.C_5^2.D_5:F_5.C_2^2$
Copy content magma:IdentifyGroup(G);
 
Order:  $1310720000=2^{21} \cdot 5^{4}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $40$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $240451$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,31,5,39,3,35,9,37)(2,32,6,40,4,36,10,38)(7,34,8,33)(11,26,13,21,17,24,16,28,12,25,14,22,18,23,15,27)(19,30)(20,29)$, $(1,24,9,25,4,22,5,30,2,23,10,26,3,21,6,29)(7,28)(8,27)(11,34,15,38,18,39,13,35,12,33,16,37,17,40,14,36)(19,31)(20,32)$, $(1,24,9,27,4,29,5,26,2,23,10,28,3,30,6,25)(7,21)(8,22)(11,38,12,37)(13,32,18,39,19,33,16,36)(14,31,17,40,20,34,15,35)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_4$ x 4, $C_2^2$ x 7
$8$:  $C_4\times C_2$ x 6, $C_2^3$
$16$:  $C_8:C_2$ x 2
$400$:  $(C_5^2 : C_8):C_2$ x 2

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

Degree 5: None

Degree 8: None

Degree 10: None

Degree 20: 20T485

Low degree siblings

There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.

Conjugacy classes

Conjugacy classes not computed

Copy content magma:ConjugacyClasses(G);
 

Character table

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed